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Erosion of solid particles in a pipe elbow containing a 90° angle is investigated by simulation methods. In the process of shale gas exploitation, the impact of solid particles carried by fluid on the inner surface wall of pipes, as well as the turbulent flow, cause the erosion of pipes, which brings about heavy economic losses for the oil and gas industry. In the impact erosion of the inner surface wall of the pipe, the worst erosion occurs at the elbow. In this study, the erosion of a pipe elbow which has been widely used in actual production is analyzed, and the influence of the fluid velocity, the solid particle size, and the wall roughness on the erosion is investigated. Additionally, the simulation results of the erosion with the rebound and freeze boundary conditions are compared, indicating that setting the freeze boundary condition could significantly improve the computational efficiency by 74% with the acceptable accuracy. In order to reduce the impact erosion in the pipe elbow containing a 90° angle, an optimal design is proposed that can reduce the maximum erosion rate by 52.4%. These results complement the research of elbow erosion and provide ideas for the optimization problem of a pipe elbow containing a 90° angle.